Problem: Express your answer as a mixed number simplified to lowest terms. $14\dfrac{1}{3}-10\dfrac{15}{17} = {?}$
Answer: Find a common denominator for the fractions: $= {14\dfrac{17}{51}}-{10\dfrac{45}{51}}$ Convert ${14\dfrac{17}{51}}$ to ${13 + \dfrac{51}{51} + \dfrac{17}{51}}$ So the problem becomes: ${13\dfrac{68}{51}}-{10\dfrac{45}{51}}$ Separate the whole numbers from the fractional parts: $= {13} + {\dfrac{68}{51}} - {10} - {\dfrac{45}{51}}$ Bring the whole numbers together and the fractions together: $= {13} - {10} + {\dfrac{68}{51}} - {\dfrac{45}{51}}$ Subtract the whole numbers: $=3 + {\dfrac{68}{51}} - {\dfrac{45}{51}}$ Subtract the fractions: $= 3+\dfrac{23}{51}$ Combine the whole and fractional parts into a mixed number: $= 3\dfrac{23}{51}$